List questions from generating-functions

Published on 22 Jun 2023 - 18:44

134

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Formula involving the Stirling numbers of the second kind

Published on 27 Mar 2026 - 22:12

13

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Reconstructing / Interpolating underlying timeseries dataset from partial sums

Published on 26 Jun 2023 - 9:17

100

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Proving the identity $\sum_{k=0}^{m} \binom{n-k}{m-k}= \binom{n+1}{m}$ .

Published on 26 Jun 2023 - 19:18

79

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Obtaining $f$ given $\sum_{i=1}^\infty f(i) \frac{1}{u-f(i)}$?

Published on 27 Jun 2023 - 5:28

73

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Using generating function to prove a combinatorical identity

Published on 27 Jun 2023 - 21:08

89

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Finding limits, possibly by generating functions

Published on 28 Jun 2023 - 11:23

132

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Using snake oil to evaluate $\sum_{k=0}^n(3k+1)\text C_n^k$

Published on 01 Apr 2026 - 9:54

385

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Log-tangent integral using exponential generating function $\int_0^{\pi/2}x\log^n(\tan x)\,dx$

Published on 04 Apr 2026 - 1:19

223

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Understanding Smirnov words in analytic combinatorics

Published on 26 Mar 2026 - 19:16

107

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How to prove Newton's identity $kh_k = \sum_{i=1}^kh_{k-i}p_i$ for symmetric polynomials?

Published on 01 Jul 2023 - 3:17

90

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Closed form for $\sum_{n=1}^{\infty}\frac{(2\log\phi)^{2n+3}B_{2n}}{2n(2n+3)!}$

Published on 26 Mar 2026 - 17:46

70

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Number of strings of length $n$ over {$x,y,z$} where $x$ and $y$ appear at least once

Published on 26 Mar 2026 - 19:20

184

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Solution to the recurrence $a_n = 2a_{n - 1} - 2^n$

Published on 04 Jul 2023 - 10:59

88

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How many graphs are there such that every vertex has degree at most 3?

Published on 10 Jul 2023 - 17:24

List Question

Do the odd coefficients of the power series for tangent form a decreasing sequence?

Formula involving the Stirling numbers of the second kind

Reconstructing / Interpolating underlying timeseries dataset from partial sums

Proving the identity $\sum_{k=0}^{m} \binom{n-k}{m-k}= \binom{n+1}{m}$ .

Obtaining $f$ given $\sum_{i=1}^\infty f(i) \frac{1}{u-f(i)}$?

Using generating function to prove a combinatorical identity

Finding limits, possibly by generating functions

Using snake oil to evaluate $\sum_{k=0}^n(3k+1)\text C_n^k$

Log-tangent integral using exponential generating function $\int_0^{\pi/2}x\log^n(\tan x)\,dx$

Understanding Smirnov words in analytic combinatorics

How to prove Newton's identity $kh_k = \sum_{i=1}^kh_{k-i}p_i$ for symmetric polynomials?

Closed form for $\sum_{n=1}^{\infty}\frac{(2\log\phi)^{2n+3}B_{2n}}{2n(2n+3)!}$

Number of strings of length $n$ over {$x,y,z$} where $x$ and $y$ appear at least once

Solution to the recurrence $a_n = 2a_{n - 1} - 2^n$

How many graphs are there such that every vertex has degree at most 3?

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